An inertia lowering control apparatus for a two-mass inertia system, the two-mass inertia system having a motor (induction motor), a load of the motor, and a flexible drive shaft having a low rigidity interconnected between the motor and load, is used to suppress an axially torsional vibration occurring on the flexible shaft in the two-mass inertia system. For example, the first-order lag filter having a transfer function as 1/(1+ST.sub.F) is added at an output portion of the Simulator Following Control section which serves as a disturbance suppression circuit together with a shaft torque estimating observer to estimate a shaft applied torque .tau..sub.S. A simulation of the above-described example indicated that even if the observer gain of the shaft torque estimating observer was relatively small, the effect of suppressing the axially torsional vibration was remarkable.